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Bremmer series that correct parabolic approximations. (English) Zbl 0313.35020

MSC:
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35C10 Series solutions to PDEs
35A35 Theoretical approximation in context of PDEs
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References:
[1] Bremmer, H, The W.K.B approximation as a first term of a geometric-optical series, Commun. pure appl. math., 4, 105, (1951) · Zbl 0043.20301
[2] Fock, V.A, Electromagnetic diffraction and propagation problems, (1960), McMillian New York
[3] Bellman, R; Kalaba, R, Functional equations, wave propagation, and invariant imbedding, J. math. mech., 8, 683, (1959) · Zbl 0090.45301
[4] {\scJ. Corones and D. W. McLaughlin}, The Parabolic Approximation in Focusing Media, to appear.
[5] Sluijter, F.W, Generalizations of the bremmer series based on physical concepts, J. math. anal. appl., 27, 282-302, (1969) · Zbl 0176.47101
[6] Sluijter, F.W, Arbitrariness of dividing the total field in an optical inhomogenous medium into direct and reversed waves, J. opt. soc. am., 60, 8, (1970)
[7] Arnaud, J.A, Nonorthogonal waveguides and resonators, Bell syst. tech. J., 49, 2311, (1970) · Zbl 0213.11503
[8] Atkinson, F.V, Wave propagation and bremmer series, J. math. anal. appl., 1, 255, (1960) · Zbl 0103.05502
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